Sign in with your new account on the xBox and download the Netflix or Hulu app. You will be asked for a gold account, but when it asks for it you can just sign back in with your previous xBox account and continue the install.

If you want to download UK Apps like iPlayer and ITV on your xBox you need to use the same steps as for the US Apps. The only difference is that you need to use a UK address when you sign-up: https://signup.live.com